Factor the quadratic expression completely. $-8x^2-15x+2=$
Since the terms in the expression do not share a common monomial factor and the coefficient on the leading $x^2$ term is not $1$, let's factor by grouping. The expression ${-8}x^2{-15}x{+2}$ is in the form ${A}x^2+{B}x+{C}$. First, we need to find two integers ${a}$ and ${b}$ such that: $\begin{cases} &{a}+{b}={B}={-15} \\\\ &{ab}={A}{C}= ({-8})({2})=-16 \end{cases}$ We find that ${a}={1}$ and ${b}={-16}$ satisfy these conditions, since ${1}+({-16})={-15}$ and $({1})({-16})=-16$. Next, we can use these values to rewrite the $x$ -term and factor by grouping. $\begin{aligned} -8x^2-15x+2&=-8x^2{-16}x+{1}x+2 \\\\ &=-8x(x+2)+1(x+2) \\\\ &=(-8x+1)(x+2) \end{aligned}$ In conclusion, $-8x^2-15x+2=(-8x+1)(x+2)$